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May 30, 2026Open Access

Solving non-homogeneous non-Linear difference and differential equations by using additive and multiplicative derivative and integral with applications

Key Points

The aim is to solve non-homogeneous non-linear difference and differential equations using discrete methods.
Utilized multiplicative discrete and continuous differential equations for solving complex equations.
Applied analytical methods for linear and non-linear equations.
Examined various applications in physics, engineering, and economics.
Provided analytical solutions for both linear and non-linear equations.
Demonstrated the effectiveness of discrete derivative in solving complex models.
Highlighted practical implications in discrete data scenarios.

Abstract

Difference equations are discrete analogy of the differential equations. These equations appearin mathematical modeling of physics and engineering problems, economic and population subjects thatdeal with discrete data and variables.In this article, we consider and solve these types of equations that are non-homogeneous and non-linear.The solving method is performed using by multiplicative discrete and continuous differential equations.The importance of this method is that by using the concept of discrete derivative, the analytical methodand analytical solutions are given to linear and non -linear non-Homogeneous difference and differentialequations.

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